It is shown that the lattice Boltzmann equation LBE corresponds to an explicit Verlet time-marching scheme for a continuum generalized Boltzmann equation with a memory delay equal to a half time step. This proves second-order accuracy of LBE with respect to this generalized equation, with no need of resorting to any implicit time-marching procedure Crank-Nicholson and associated nonlinear variable transformations. It is also shown, and numerically demonstrated, that this equivalence is not only formal, but it also translates into a complete equivalence of the corresponding computational schemes with respect to the hydrodynamic equa- tions. Second-order accuracy with respect to the continuum kinetic equation is also numerically demonstrated for the case of the Taylor-Green vortex. It is pointed out that the equivalence is however broken for the case in which mass and/or momentum are not conserved, such as for chemically reactive flows and mixtures. For such flows, the time-centered implicit formulation may indeed offer a better numerical accuracy.
|Titolo:||Three ways to lattice Boltzmann: A unified time-marching picture|
|Data di pubblicazione:||2010|
|Digital Object Identifier (DOI):||10.1103/PhysRevE.81.016311|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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|preprint_Asinari_PRE_2010b.pdf||1. Pre-print||PUBBLICO - Tutti i diritti riservati||Visibile a tuttiVisualizza/Apri|
|PhysRevE.81.016311.pdf||Three ways to lattice Boltzmann||2. Post-print||PUBBLICO - Tutti i diritti riservati||Visibile a tuttiVisualizza/Apri|